A dimension reduction in neural network using copula matrix

Abstract

In prediction analysis, there may exist some nonlinear relations between the exploratory variables, which are not captured by traditional correlation-based linear models such as multiple regression, principal component regression, and so on. In this work, we employ a copula matrix to extract principal components of a set of variables which are pair-wisely associated with a copula. By estimating the pairwise copula and its corresponding parameter(s), we suggest an optimization method to extract principal components from a matrix which contains some pairwise measures of association. We use these components as inputs of an artificial neural network to make a more accurate prediction. We test our proposed method using a simulation study and use it to carry out a more accurate prediction in an AIDS as well as a COVID-19 dataset. To increase the reliability of results, we employ a cross-validation technique.